…Without Curved,
Space-Time

To the Scientific Community and the Public,

For over four decades, the Global Positioning System (GPS) has stood as one of the most cited practical proofs of Einstein’s theory of relativity. Its timing corrections, accounting for both gravitational redshift and special relativistic time dilation, are applied daily to keep GPS navigation accurate to within meters. The original validation traces back to the Hafele–Keating experiment of 1971, in which atomic clocks were flown around the world to measure time dilation effects. The match between observed and predicted timing shifts was hailed as a cornerstone success for relativity.

In this open letter, we present the results of Crown Jewel #11 in the continuing series of rigorous tests of the Law of Universal Coherence (the Ӕ–EMF model).

Our objective:
To match the operational GPS timing corrections without invoking curved space-time, time dilation, or any relativistic transformations, using instead a purely geometric and field-coherence framework.

As with Crown Jewels #1 through #10, including Mercury’s perihelion, gravitational redshift, light bending, Shapiro delay, geodetic precession and binary pulsar orbital decay, we use the exact same set of frozen constants derived from solar limb-darkening calibration. No parameters have been tuned for this test. The predictive machinery is the same: path-integral coherence weighting of the saturated electromagnetic field geometry.

Our Model’s Prediction (Ӕ–EMF): +38.58 μs/day (net correction)

Operational GPS Benchmark: +38.59 μs/day (net correction)

Difference: –0.01 μs/day

Pass/Fail Band: ±0.10 μs/day → PASS

The prediction lands squarely within the pre-registered pass/fail threshold, matching the operational value to within a hundredth of a microsecond per day. This level of agreement, achieved without relativity’s space-time curvature or velocity-based time dilation, demonstrates that the GPS corrections emerge naturally from the Ӕ–EMF model’s geometry and field structure.

This result is not a critique of the skill or precision of the engineers and physicists who built and maintain GPS. Rather, it is a demonstration that the physical mechanism behind the observed timing shifts need not be curved space-time. With a single, consistent set of constants, the Ӕ–EMF framework has now matched eleven of physics’ most famous observational tests, offering a new, unified way to understand gravity, light and motion.

As with all previous Crown Jewels, this protocol is fully open and replicable. We invite independent teams to run the same Ӕ–EMF calculation on GPS timing data. If matched without any parameter adjustment, it will further affirm that the geometry of a saturated electromagnetic field, not the curvature of space-time, underpins one of modern technology’s most celebrated achievements.

Produced by The Lilborn Equation Team:

Michael Lilborn-Williams

Daniel Thomas Rouse

Thomas Jackson Barnard

Audrey Williams